The Labour leader told conference delegates in Brighton that their party was a “government in waiting” which is campaign-ready for another snap election.
But he was accused of indulging in “fantasy economics” at the end of a conference which has seen the cost of Labour’s redistributive agenda spiral by billions of pounds.
And business leaders responded to the speech with a plea that they are “not the enemy”.
Addressing cheering delegates who have him a two-minute standing ovation before he began speaking, Mr Corbyn said: “Today’s centre ground is certainly not where it was twenty or thirty years ago.
“A new consensus is emerging from the great economic crash and the years of austerity, when people started to find political voice for their hopes for something different and better.”
He went on: “This is the real centre of gravity of British politics. We are now the political mainstream.
“Our manifesto and our policies are popular because that is what most people in our country actually want, not what they’re told they should want.”
The Labour leader drew on the Grenfell Tower disaster and sexual grooming of girls by gangs as examples of scandals that have taken place because ordinary people have been shut out of politics.
And he said Labour would bring forward rent controls and measures to ensure regeneration no longer results in gentrification, with tenants forced to make way for developments that drive up rents and push them out of their neighbourhoods.
Mr Corbyn said a Labour government would give the public more control over their workplaces, schools and hospitals and break the consensus “that the big decisions should be left to the elite”.
“Democracy has to mean much more than that,” he said. “It must mean listening to people outside of election time.
“Not just the rich and powerful who are used to calling the shots, but to those at the sharp end who really know what’s going on.”
Calling for the pay cap to be lifted for all public sector workers, Mr Corbyn said: “Everyone praises them. But it is Labour that values them and is prepared to give them the pay rise they deserve and protect the services they provide.”
Closing a conference with a markedly more positive atmosphere, the Labour leader praised his party’s newfound unity and said: “I hope we have left our own divisions behind.”
But his message was blunted when he thanked Kezia Dugdale for her service as Scottish leader, with Labour north of the border engulfed in a new row between opposing factions.
Stephen Martin, the director general of the Institute of Directors, said: “There was plenty of criticism for privatised utilities, for big companies and for employers in general, but it would be very worrying if the Leader of the Opposition really saw nothing positive in Britain’s business community.
“Labour may see themselves as a government in waiting, but if they are to govern, they will need to recognise that business is not the enemy.”
And Alex Marshall, the director general of the British Chambers of Commerce, warned businesses were “already worried about widespread state intervention, nationalisation, and the radical increases in taxes and costs they could face under a future Labour government.”
He said: "There is a rising concern amongst businesses about the two largest parties in Westminster, with one flirting with fantasy economics while the other engages in an unedifying playground bust-up.”
The Labour leader set his own course on foreign policy, rejecting military intervention and promising to “end the oppression of the Palestinian people” by working towards a two-state solution in the Middle East.
Mr Corbyn sought to embarrass the Prime Minister over her ties to Donald Trump amid fears of a tit-for-tat trade dispute between the US and the UK that threatens thousands of jobs at aircraft manufacturer Bombardier in Northern Ireland.
He condemned President Trump’s UN speech threatening to “totally destroy” North Korea as “deeply disturbing” and criticized the US’s withdrawal from the Paris climate accords.
“Our government has a responsibility. It cannot meekly go along with this dangerous course,” Mr Corbyn said.
“If the special relationship means anything, it must mean that we can say to Washington: that way is the wrong way.”
And he called on Aung San Suu Kyi to “end the violence now” against the Rohingya Muslims of Myanmar and protect her legacy as “a champion of democracy and human rights”.